The decision means that Wembley will stage seven games in total - the final, both semi-finals, a last-16 match and three group games - resulting in the biggest festival of global football in the country since Euro 96.
London will host seven games in total - including the final and one semi-final - after Brussels was stripped of its host city status.
"They still don't have the documents".
The opening game will be held at Stadio Olimpico - home of AS Roma - in Rome on June 12, 2020 and could feature either or both of Italy and Azerbaijan.
"Experts from administration had the opinion it was a high risk for UEFA if we wait". "If the answer had been no, it would have been a problem for us to find a new stadium".
UEFA president Aleksander Ceferin said that the four matches due to be staged in Brusselsm - three group games and one last-16 match - would be played at Wembley instead, in addition to the two semi-finals and final already scheduled to be played there.
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However they said UEFA's decision "does not necessarily signify the end of the stadium project". "We absolutely need a new 45,000-seat stadium and we hope that the competent ministers will grant the permit in January so that a stadium for the 21st century can finally be built in our country".
Khan said: "It speaks volumes about our great city that London has been awarded an additional four Euro 2020 matches, reinforcing the capital's reputation as the sporting capital of the world".
Bilbao and Dublin were paired together.in Group E.
The decision is a blow to the Wales FA and Swedish FA, which had lobbied UEFA to take Belgium's place as a group-stage host nation. None of the hosts qualify automatically.
'UEFA ranked the Champions League final as one of their best events and praised the way in which the Cardiff 2017 local organising committee delivered the showpiece.